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The Angstrom wavelength exponent alpha, which is the slope of the logarithm of aerosol optical depth (tau(a)) versus the logarithm of wavelength (lambda), is commonly used to characterize the wavelength dependence of tau(a) and to provide some basic information on the aerosol size distribution. This parameter is frequently computed from the spectral measurements of both ground-based sunphotometers and from satellite and aircraft remote sensing retrievals. However, spectral variation of alpha is typically not considered in the analysis and comparison of values from different techniques. We analyze the spectral measurements of tau(a) from 340 to 1020 nm obtained from ground-based Aerosol Robotic Network radiometers located in various locations where either biomass burning, urban, or desert dust aerosols are prevalent. Aerosol size distribution retrievals obtained from combined solar extinction and sky radiance measurements are also utilized in the analysis. These data show that there is significant curvature in the ln tau(a) versus ln lambda relationship for aerosol size distributions dominated by accumulation mode aerosols (biomass burning and urban). Mie theory calculations of alpha for biomass burning smoke (for a case of aged smoke at high optical depth) agree well with observations, confirming that large spectral variations in a are due to the dominance of accumulation mode aerosols, A second order polynomial fit to the ln tau(a) versus ln lambda data provides excellent agreement with differences in tau(a) of the order of the uncertainty in the measurements (similar to 0.01-0.02). The significant curvature in ln tau(a) versus ln lambda for high optical depth accumulation mode dominated aerosols results in alpha values differing by a factor of 3-5 from 340 to 870 nm. We characterize the curvature in ln tau(a) versus ln lambda by the second derivative alpha’ and suggest that this parameter be utilized in conjunction with alpha to characterize the spectral dependence of tau(a). The second derivative of ln tau(a) versus ln lambda gives an indication of the relative influence of accumulation mode versus coarse mode particles on optical properties.